Question: Express this quotient in scientific notation: ${\frac{1.050\times 10^{-7}} {3.0\times 10^{-5}}}$
Start by collecting like terms together. $= {\frac{1.050} {3.0}} \times{\frac{10^{-7}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.35 \times 10^{-7\,-\,-5}$ $= 0.35 \times 10^{-2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.35$ is the same as $3.50 \div 10$ , or $3.50 \times 10^{-1}$ $ = {3.50 \times 10^{-1}} \times 10^{-2} $ $= 3.50\times 10^{-3}$